The city’s fleet of yellow, green and livery cabs get mere once-over safety inspections by overworked TLC staffers who are pressured by management to push the cars through at lightning speed, whistleblowers told The Post.

Fed-up inspectors face retaliation from TLC brass — including losing their jobs — if they take too much time scrutinizing the city’s green and yellow taxis and livery cabs in about 113,000 inspections, the sources said.

There are only 42 officers — 20 of whom are provisional — and 13 supervisors to evaluate all those cars at the TLC’s sole cab-safety inspection center in Woodside, Queens.

“We’re always pushed. We’re rushed,” said one source. “To force someone to rush through an inspection is dangerous. It’s a disservice to the public.”

Despite their small numbers, the crews are responsible for inspecting yellow taxis three times a year, green cabs twice a year, and livery cars every other year.

Inspectors said that four officers in a lane get between 12 and 20 minutes to evaluate a car, but they need up to 40 minutes to do the job properly, sources said.

Officers told The Post that if they are too careful when inspecting the taxis, they are bullied with bad shift changes — such as when their bosses know they need to be off to pick up their kids.

Provisional workers who are too thorough are threatened with firing, sources added.

“If you’re working at your own pace, they tell you, ‘You’re moving too [slow]. Pick it up,’ ” said a source.

They will also be in charge of inspecting 6,000 additional green cabs, whose permits will start being issued in August.

“Inspectors should have enough time to make sure the cars go out safely, to ensure the public of their safety,” said Randy Klein, assistant director of Teamsters Local 237. “And assure the inspections are as professional as possible.”

Meanwhile, the inspectors are responsible at the end of the day for the cabs they inspect.

“If something happens to the car, it comes back to me,” said a source.

“The job will throw you under the bus.”

A TLC spokesman said the city’s taxis are safely inspected.

“Our inspection process is meticulously overseen, and we are confident that every vehicle coming off the line is among the safest on the road,” Allan Fromberg said. “We are grateful to Local 237 for sharing these workplace issues with us, and we look forward to working with them.”

Officials added that the agency has hired eight officers in the last year and a half for that division, and that three new ones are beginning training tomorrow.

New braking equipment has also been installed that makes inspections easier.

But abuse and low pay of the officers, who make about the same or less than cabbies, makes it very hard for the city to keep them, inspectors said.

“I don’t mind working hard,” a source said. “But what about quality and public safety?”